PSU shuts off computer

I recently bought a new Gateway computer and for the last month it's been shutting off randomly. Sometimes it'll be on for about 20 minutes sometimes it'll shut off before it even finishes loading Windows. I don't have any type of warranty on the computer and I know for a fact that it's the PSU or some problem inside the PSU. I know this because I changed the PSU for my friends and it didn't shut off in 5 days I had it in. As soon as I plugged mine back in it shut off in 5 minutes. I have more important bills and expenses right now so I can't exactly afford a new PSU so I was hoping someone could give help me find out what is going on. Most of the problems I see other ppl have like bad caps seem to shut off computers and won't let the start up. Mine will turn on but won't last long so I don't know what it could be. I installed the PSU from my dads computer and my computer has been without problems for 3 days so I'm sure it's a problem with my PSU but I have no idea what it could be? I'm still somewhat new to this kind of stuff. I'm no expert but I am able to do most basic things like replacing the PSU and that sort of thing so I'm hoping the problem is something I could fix because like I said before I don't have the money to buy a $50 PSU right now (just foung out my wife is pregnant oh ya!!) but I would like to have my computer up even though it's not my main priority right now. some basic info- it's a Gateway LX6810, 8GB Ram, 640 GB HD, 1GB Graphics Card... (oh the PSU model number is PS-6401-3). I'd just like to know what kind of problems in a PSU could cause a computer to turn on for a while but shut off abruptly in a few minutes (when it starts it comes up with the safe mode thing asking if I want to start Windows normally. only thing that comes to my mind would be overheating but the fan works and I've removed it and it doesnt seem very hot but I am a newbie so I don't know too much. Plz I would really appreciate any help anyone could give me, thank you and Happy Holidays!

P.S. Sorry for all the mispelling I had to type this fast before my computer turns off